Question

A 28 cm wrench applies 53 N of force to loosen a bolt when force is applied at the end in a perpendicular manner. What force is required if the same torque is applied at a 53° angle? Answers:
106 N
86 N
96 N
118 N

Answer 1

Answer:

66.42 N

Explanation:

Torque is defined as the product of force and the perpendicular distance.

$\tau =r\times F\times Sin\theta$

Where, r be the distance, f be the force and θ be the angle between the force vector and the distance vector

Case I :

F = 53 N, r = 28 cm = 0.28 m, θ = 90°

So, $\tau_{1} =0.28 \times 53\times Sin90$

$\tau _{1}=14.84 Nm$

case II :

F = ?, r = 0.28 m, θ = 53°

Let the force be F for the same toque.

$\tau_{1} =0.28 \times F\times Sin53$

$14.84 Nm=0.28\times F\times Sin53$

F = 66.42 N

Thus, the force required is 66.42 N.